I had the same 45% reset issue. To get past that, you need to give "Nearby Devices" permission to "Google Play Services", then the watch will complete the setup.
I also noticed that when the watch manager (or Buds manager) is downloaded and installed, Android 13 seems to disable the allow feature for some permissions - you'll know that when the enable button is grey out, or when you try to toggle on, you get a message saying something along the lines of "for your security, this has been disabled". (Is this because the Wear App is installing rather than Play store ?, Anyway..) If you go into the Apps, then permissions, there's a three dot menu button in the upper right where you can enable the restricted permission. This will let you set the permission.
The only issue I believe I have now, is that since the GPS are in the "sandbox" user profile, whenever I switch out to the main owner profile, the watch bluetooth connection disconnects. I'm presuming that the Wear app or watch manager are being put to sleep, but I haven't found a way to keep the connection alive.